Nonconvex TGV-Shearlet Based Model for Compressive Sensing

Abstract

Compressive sensing (CS), an area of signal processing, refers to the reconstruction of sparse or compressible signals from a fewer measurement. When we solve energy functional minimization problem for CS, the model consists of the data fidelity term and the regularization term. The regularization term is of importance as well as data fidelity term. In this thesis, we propose CS model by employing a hybrid of nonconvex total generalized variation (NTGV) and shearlet transform as a regularization tool. NTGV and shearlet transform behave complementary each other in CS problem as a regularization tool. Moreover, this thesis also proposes a numerical algorithm for proposed NTGV-Shearlet regularization based model by adopting iteratively reweighted L1 (IRL1) algorithm, one of the nonconvex optimization algorithms. Alternating direction method of multipliers, a well-known convex optimization problem, is also used to solve inner convex problem of our proposed model. We compare numerical results of our NTGV-Shearlet based CS model experiments to those of three other closely related state-of-the-art regularization tool based CS models experiments. Numerical results show that our NTGV-Shearlet based CS model outperforms other three CS models both visually and in terms of peak signal-to-noise ratio (PSNR).